Depends on a lot of things.
- What is the utility? How important is it, and are there non-Java alternatives?
- Why are you hesitating to install Java?
- What is the security profile of the machine?
- Sun Java or the one from your Linux distro (which is automatically updated)?
It's basically a tradeoff between the cost and the benefit. Java, like all apps, has security flaws. Sun updates their JVM every now and then and the Linux vendors that ship Java also do the same. How do you plan to push updates to this machine? How important is it? If the machine has proper firewalls and limited network daemons running, Java as an interpreter on the disk is probably not much of a hazard. Java typically doesn't run as root.
Almost any arguments that can be made about Java can be made about Perl, Mono, GCC, or any software that can run arbitrary code. Furthermore most Linux software is typically shipped by a distro, so you can often rely on the distro's updates to keep things secure. Sun Java, in this case, would be the same as any third party software. Does it matter if this third-party utility requires a library that happens to be Java? Maybe not.
The scenario is slightly different if you are talking about Java running a service application, such as Tomcat or JBoss, where Java is then listening to the network. In that case the security risk is higher. But you have the same security risks with any network-facing application such as apache or ssh.